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Funktion: f(x) = 0.75·x(x-6)2, Df = R, Wf = R, Polynom 3. Grades (Produktform), Funktion punktsymmetrisch zum Punkt W(2|12), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -1920 | 432 | -63 | 4.5 | |
-9.5 | -1711.7812 | 401.06 | -60.75 | 4.5 | |
-9 | -1518.75 | 371.25 | -58.5 | 4.5 | |
-8.5 | -1340.3437 | 342.56 | -56.25 | 4.5 | |
-8 | -1176 | 315 | -54 | 4.5 | |
-7.5 | -1025.1562 | 288.56 | -51.75 | 4.5 | |
-7 | -887.25 | 263.25 | -49.5 | 4.5 | |
-6.5 | -761.7187 | 239.06 | -47.25 | 4.5 | |
-6 | -648 | 216 | -45 | 4.5 | |
-5.5 | -545.5312 | 194.06 | -42.75 | 4.5 | |
-5 | -453.75 | 173.25 | -40.5 | 4.5 | |
-4.5 | -372.0937 | 153.56 | -38.25 | 4.5 | |
-4 | -300 | 135 | -36 | 4.5 | |
-3.5 | -236.9062 | 117.56 | -33.75 | 4.5 | |
-3 | -182.25 | 101.25 | -31.5 | 4.5 | |
-2.5 | -135.4687 | 86.06 | -29.25 | 4.5 | |
-2 | -96 | 72 | -27 | 4.5 | |
-1.5 | -63.2812 | 59.06 | -24.75 | 4.5 | |
-1 | -36.75 | 47.25 | -22.5 | 4.5 | |
-0.5 | -15.8437 | 36.56 | -20.25 | 4.5 | |
0 | 0 | 27 | -18 | 4.5 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | 11.3438 | 18.56 | -15.75 | 4.5 | |
1 | 18.75 | 11.25 | -13.5 | 4.5 | |
1.5 | 22.7813 | 5.06 | -11.25 | 4.5 | |
2 | 24 | 0 | -9 | 4.5 | Hochpunkt H(2|24) |
2.5 | 22.9688 | -3.94 | -6.75 | 4.5 | |
3 | 20.25 | -6.75 | -4.5 | 4.5 | |
3.5 | 16.4063 | -8.44 | -2.25 | 4.5 | |
4 | 12 | -9 | 0 | 4.5 | Wendepunkt W(4|12) |
4.5 | 7.5938 | -8.44 | 2.25 | 4.5 | |
5 | 3.75 | -6.75 | 4.5 | 4.5 | |
5.5 | 1.0313 | -3.94 | 6.75 | 4.5 | |
6 | 0 | 0 | 9 | 4.5 | Tiefpunkt T(6|0) |
6.5 | 1.2188 | 5.06 | 11.25 | 4.5 | |
7 | 5.25 | 11.25 | 13.5 | 4.5 | |
7.5 | 12.6563 | 18.56 | 15.75 | 4.5 | |
8 | 24 | 27 | 18 | 4.5 | |
8.5 | 39.8438 | 36.56 | 20.25 | 4.5 | |
9 | 60.75 | 47.25 | 22.5 | 4.5 | |
9.5 | 87.2813 | 59.06 | 24.75 | 4.5 | |
10 | 120 | 72 | 27 | 4.5 | |
Graph: | |||||
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann